Physics 9702 · AS & A Level · Equilibrium of forces

Equilibrium of forces — practice question

A metal wire connects a sphere to the horizontal bed at the bottom of a river, as illustrated in Fig. 2.1. The sphere is completely below the water surface and in equilibrium, with the wire making an angle of $68^\circ$ to the horizontal surface. The sphere’s weight is $32\,\text{N}$. The upthrust on the sphere is $280\,\text{N}$. The water has density $1.0 \times 10^3\,\text{kg m}^{-3}$. Assume that the force on the sphere caused by the water flow acts horizontally.
(a)[2]

Using the vertical components of the forces, find the tension in the wire.

(b(i))[1]

Find the volume of the sphere.

(b(ii))[2]

Find the density of the sphere.

(c)[3]

The centre of the sphere starts at a height of $6.2\,\text{m}$ above the horizontal surface. The water speed then rises, making the sphere move to another position. As a result, the sphere’s gravitational potential energy falls by $77\,\text{J}$. Calculate the final height of the centre of the sphere above the horizontal surface.

(d(i))[1]

As described in (c), the sphere’s movement makes the wire extend further. The wire follows Hooke's law. State a symbol equation that relates the tension $T$ in the wire to its extension $x$. Define any other symbol that you use.

(d(ii))[2]

Before the sphere moved, the wire had an initial elastic potential energy of $0.65\,\text{J}$. The sphere’s change of position causes the wire extension to double. Calculate the final elastic potential energy of the wire after the sphere has moved.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Valid equation $T \sin 68^\circ + 32 = 280$” …

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI